I am testing the same model twice; the outcome variable is different for each model, but the predictor variables are the same (Outcome for Model One is Intention to use a face-to-face support service, and outcome variable for Model Two is Intention to use a telephone support service). When I tested the models, the fit indices for both indicated a very good fit to the data. On the second model, however, for one of the variables, no significant paths are evident (to the outcome variable or any other IV). I would have expected the relationships to be significant based on correlations. When I remove this variable from the model, the fit is no longer acceptable. Do you have any suggestions of what might be happening here?

I am testing a SEM model with 3 latent constructs which yield good model fits in measurement part. When I add the ON statement to test its structural part, the path between IV & DV and Mediator & DV no longer exist. Anything I should further check or to improve the model? and what does it means by the not significant path in this case? thank you very much.